Question

If alpha and beta are roots of quadratic equation 2x^2 – 3x + 1 = 0, then find the equation whose roots are 2alpha/beta and 2beta/alpha

Answer 1

Step-by-step explanation:

2x^2 - 3x + 1 = 0

2x^2 - 2x - x +1 = 0

2x*(x -1) - 1*(x-1) =0

(2x-1)*(x-1) =0

alpha= 1/2 & beta = 1

2*alpha/beta = (2*1/2)/1 = 1

2*beta/alpha = 2*1/(1/2) = 4

so the equation will be

(x-1)*(x-4) = 0

x^2 - 4x -x +4 =0

x^2 - 5x +4 =0

which is the required equation